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# Riddle and Puzzle Thread - Page 3

@billchao is correct. The riddle does NOT say it has to be equal number of heads UP.

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Quote:
Originally Posted by Yukari

@billchao is correct. The riddle does NOT say it has to be equal number of heads UP.

It is what it says, but I think it's just either a typo or an oversight.

I'm pretty stumped on this one. Didn't @iacas say he thought he had it figured out?

Quote:
Originally Posted by mdl

You are given 99 coins that are heads up, and an unknown number of coins that are tails up. You are blindfolded and somehow can't feel the difference between the heads and tails sides of the coins. You can count the coins, put them in arbitrary many piles, flip whichever coins you want, but remember, when you flip and when you sort, you DO NOT know which ones are heads up, which are tails up. In the end, you must end up with just two piles, each containing an equal number of heads. How do you do this?

I struggled with this one for awhile but then I realized I was misreading it as saying "and an unknown number of coins that are heads or tails up." But it just says "tails up."

Duh.

And all we care about in the end is that the number that are heads up is the same - we don't care about how many are tails up in either of the piles. I also think people get confused by the number 99 being odd…

But anyway: since 99 coins are heads up, we have this:

 Coin Side Number Heads 99 Tails ???

You can do this in two moves, I believe.

First, pull out 99 coins into Pile B (we'll call the original pile Pile A).

Pile B will contain X heads up coins. This is the number, of the 99, that are heads up.

Pile A will contain 99 - X heads up coins. It started with 99, and we remove between 0 and 99 heads up coins.

Since we don't care at all about the tails, we can look at the heads up only, and we have:

 Pile A Pile B Before: 99 coins heads up Before: 0 coins heads up After: 99-X coins heads up After: 99 coins, X heads up

For the heck of it, let's just say we took out 66 heads up coins. That means we also pulled out 33 tails up coins. That would make the tables look like this:

 Pile A Pile B 99-66, leaving 33 coins heads up 66 heads up, 33 tails up

The red gives away the answer. Flip all 99 coins in Pile B. The number of tails up in Pile B equals the number of heads up that you started with (99) minus the number of heads up that you took away (i.e. what remains in Pile A).

It works for any number from 0 to 99. If you pull 99 coins over that are tails up, flip them all, they'll match the original 99 heads up coins that you somehow avoided getting into Pile B. If you pull all 99 coins that are heads up, you'll flip them all to tails up, and the number of heads will be 0.

If you pull 98 heads over, leaving one in Pile A, the one tails up coin will be converted. If you pull 1 heads over, leaving 98 in Pile A, the 98 tails that came with it will convert.

The only way this fails - because you can't create two piles using my method - is if there are ONLY 99 heads up coins and NO tails up coins to start… but even then you'll have 0 heads up.

Pull coins out of the pile till there are only 99 left, then flip those 99.

Quote:
Originally Posted by M2R

Pull coins out of the pile till there are only 99 left, then flip those 99.

That's kind of the opposite of my solution, but requires more work (because you have to count all of the coins first to know how many there are).

Quote:
Originally Posted by iacas

That's kind of the opposite of my solution, but requires more work (because you have to count all of the coins first to know how many there are).

It is your solution, just explained in a different way as your explanation confused me ... again but these things happen. In the case of zero tails ends up with two piles with zero heads and one pile has zero coins as well.

Here's an old one:

A friend of yours is a big gambler. He decides one day to bet you everything you have for everything he has in a simple game. You're a gambler too so you go along.

The rules of the game are simple. You're each given identically sized poker chips and a flat, rectangular table on which to play. You'll alternate turns placing one poker chip down per turn, with the stipulation that the poker chip must rest completely flat on the table (no hanging over the edge, no overlapping other chips, no standing poker chips on their edges - you also can't move any poker chips once placed), and that you lose when you cannot make a legal play.

Your friend (stupidly) offers you the choice of deciding who makes the first move OR to pick the size of the table. He'll make the other choice.

Which do choice do you take, what do you choose, and why?

Quote:
Originally Posted by iacas

Here's an old one:

A friend of yours is a big gambler. He decides one day to bet you everything you have for everything he has in a simple game. You're a gambler too so you go along.

The rules of the game are simple. You're each given identically sized poker chips and a flat, rectangular table on which to play. You'll alternate turns placing one poker chip down per turn, with the stipulation that the poker chip must rest completely flat on the table (no hanging over the edge, no overlapping other chips, no standing poker chips on their edges - you also can't move any poker chips once placed), and that you lose when you cannot make a legal play.

Your friend (stupidly) offers you the choice of deciding who makes the first move OR to pick the size of the table. He'll make the other choice.

Which do choice do you take, what do you choose, and why?

Choose the table size? Then you can choose a table that will only fit two chips?

That was my first though, then I realized he could place it in the middle leaving me no move. Then I realized the answer would be to choose the table size and choose a table too small to legally place a chip.

I don't know if I'm right so I'll put my riddle in a spoiler:

Warning: Spoiler! (Click to show)
A barrel of water weighs 20 lbs, what do you need to add to it to make it weigh 15 lbs?
Quote:
Originally Posted by Ernest Jones

Choose the table size? Then you can choose a table that will only fit two chips?

That was my first though, then I realized he could place it in the middle leaving me no move. Then I realized the answer would be to choose the table size and choose a table too small to legally place a chip.

Then he would choose to let you go first.......
I let him choose the table size, then technically I should be able to calculate how many moves are available and then choose to play first or second. I'm sure there is a trick answer but that is what I would do!
Quote:
Originally Posted by David in FL

Then he would choose to let you go first.......

oh

In order not to give anything away by giving any partial credit, I'll just say that nobody has given the fully correct answer yet.

Quote:
Originally Posted by Abu3baid

I let him choose the table size, then technically I should be able to calculate how many moves are available and then choose to play first or second. I'm sure there is a trick answer but that is what I would do!

Specifically, that won't work because you can't force a certain spacing. Either player could put some chips right against other chips, while spacing some others almost a full poker chip size away.

Answer to Ernest's Question (Click to show)

Quote:
Originally Posted by iacas

In order not to give anything away by giving any partial credit, I'll just say that nobody has given the fully correct answer yet.

Specifically, that won't work because you can't force a certain spacing. Either player could put some chips right against other chips, while spacing some others almost a full poker chip size away.
Answer to Ernest's Question (Click to show)

Yes, I agree... Then in that casei will pick the table size and make it so big that it will never take the amount of chips we have and that way no one wins and I keep my stuff... :) not fun i know!
Quote:
Originally Posted by Abu3baid

Yes, I agree... Then in that casei will pick the table size and make it so big that it will never take the amount of chips we have and that way no one wins and I keep my stuff... :) not fun i know!

Uhhhh, no. You both have an infinite number of available chips.

Besides, you want his stuff, and you can guarantee getting it if you choose wisely.

Chose "who makes the first move" for the reason EJ said "oh", leaves you are holding all the cards.

If it's zero chip size he plays first, if it's two chip size you play first and play the middle to muck each end, if it is three chip size you play first and play the middle forcing him to play either end, other than that play first and when it gets to the last two or three squares make one of those plays.

Quote:
Originally Posted by M2R

If it's zero chip size he plays first, if it's two chip size you play first and play the middle to muck each end, if it is three chip size you play first and play the middle forcing him to play either end, other than that play first and when it gets to the last two or three squares make one of those plays.

I don't think you understood the question. Plus you don't know what size the table is unless you pick it. If you choose to decide who goes first, then your opponent gets to pick the table size.

Still working it.  but I have to pick table size.

1 - If I decide to go first, he will just make a table smaller than the chips.

2 - If I decide to go second, he will just make a table big enough for one

Again, my smart alec decision is "I'll pick the table size, I'll let you know as soon as you decide to move 1st or 2nd"

(I know this isn't the intent.)

So now to logic out the table size.......(I had to coin puzzle figured out last night.....too late to get it in here.  once figured out that the piles can be different sizes and we don't care if the tails are equal or not it just became a matter of figuring out how to trade equal numbers of flips - works easy by starting with smaller number assumptions)

actually - as long as I have his info first, I don't much care which criteria I get to constrain

Guys these are tables and poker chips. A table that couldn't even fit two poker chips is not a table. I don't know what it is but it's not a table.

It's a normal table. I don't care if it's a small coffee table or a banquet table that seats 100 people. It's a "table."
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